Animate location (or strength?) of alpha / opacity mask to suggest motion along arrows
I would start by adding something like this node set up where my Diffuse BSDF is your Diffuse shader after the Trade_Winds11 Image Texture and it all goes into the following Mix node.

In my example animating the Z Location in the Mapping node will cause that black line (hopefully alpha as it is running through a transparent shader) to move up or down. You can really play with the Mapping node to get the lines from the wave texture to move how you'd like.

I hope this helps.